It seems like it’s a combination of Mr. Threehorn and Grandpa Longneck. Usually, the Great Valley goes with Mr. Threehorn and whatever he says, but many times, Grandpa Longneck is able to talk them out of Mr. Threehorn’s, usually bad, idea.
Thus, if Grandpa Longneck dies first, the Great Valley might be run more bullheadedly, but if Mr. Threehorn dies first, the Great Valley will be run more reasonably.
Of course, despite what they said about everyone making the decisions together, it seems that the rest of the group either decides on either Mr. Threehorn’s ideas or Grandpa Longneck’s ideas. They have yet, as far as I can recall, to reject ideas from BOTH of them and propse their own. Indeed, Pterano seems to be the only one that got some of them to go against BOTH Grandpa Longneck and Mr. Threehorn.
Thus, all one would have to do to become dictator of the Great Valley is convince Mr. Threehorn and Grandpa and Grandma Longeck to give over power to you as the sole decision maker and the others would all likely back them. Getting Mr. Threehorn to go along shouldn’t be too hard, as long as you blame things on racial lines, etc. Getting Grandpa and Grandma Lognenck to go along would be harder. The only thing I can think of is that it could work if the item or the “crisis” issue was Sharptooth related. Both Grandpa Longneck and Grandma Longneck seem to have a bias against Sharpteeth, thinking them not really smart, and both Grandpa Longneck and Doc killed these Sharpteeth in a pretty cold way in movie VI. Also, if their son in law Bron were there and the issue were Sharptooth related, he’d probably also be pushing Grandpa and Grandma Longneck to go along with the “solution”.